Axelrod made the remarks in an exclusive interview on "This Week with Christiane Amanpour."

Senate Minority Leader Mitch McConnell, also appearing exclusively on "This Week" fired back. "Nothing's being held hostage to anything. It was the Democrats themselves who decided not to have this debate."

Axelrod criticized the House Republicans' "Pledge to America," saying, "It would borrow $700 billion to cut taxes for the very wealthy, add trillions of dollars to the deficits." Republicans, he added, are "going to have to explain to their constituents why they're holding up tax cuts for the middle class."

McConnell said that letting tax cuts expire will hurt the economy, but would not say what spending cuts he would make to pay for extending the tax cuts. "Senate Republicans," he said, "offered to freeze the top line on next year's appropriations at essentially what we spent this year."

Amanpour pressed Axelrod on whether Democrats could pass an extension of middle-class tax cuts during a lame duck session of Congress. "We're going to get that done," he said, "one way or another we're going to get it done."

McConnell wouldn't say whether Republicans would compromise on taxes after the mid-term election. "What might happen down the road is not the subject today," he said.